An Introduction to 3D Vector Analysis

This is the beginning of an online course to get to grips with 3D vectors for anyone who wants to learn. Most of the material is about UK A-level difficulty, so if you're studying a maths course involving vectors I hope working through it won't harm your grades:) Also if you're interested in related topics, such as 3D graphics programming or Newtonian mechanics, I hope you'll find something useful or interesting.

Contents

Good luck with the course!...

• 3D Vectors
• The Dot Product
• The Cross Product
• The Vector Equation of a Line
• The Vector Equation of a Plane
• The Point of Intersection of a Line and a Plane
• Some Shortest Distance Calculations
• Coordinate Systems
• An introduction to parametric curves

Links to the applets used in the course

• Great circle applet
• Molecular modeller applet
• Dot product applet
• Cross product applet
• Dodecahedron applet
• Distance to a plane applet
• Parametric curves applet
• Parametric surfaces applet

Apologies for the extremely slow progress - finals seem to be taking up most of my time at the moment. Many thanks for the encouragement though, and I hope I can get round to improving the site before long.

In progress...

• An applet to help explain parametric vector equations - curves in 3D space.
• Trajectories - Keplers' laws of planetary motion and conic sections.
• Linear transformations between vector spaces, rotations, reflections, scalings...
• The intersection of 3 planes
• Volume of a parallelepiped (used in crystallography and xray diffraction)
• Eigenvalues and eigenvectors
• Complex numbers (isomorphic to 2D vectors)

If you found the above simple and are curious about what a vector really is here's a page introducing the concept of a vector space.

Please e-mail me (Paul Kirby) if you have any suggestions, improvements, find any errors, think some part is unclear, or just want to:)